10
QuizMultiple Choice

N/A — Exam

Question 10 • Geometry: Concepts and Connections

Which expression represents the volume, in cubic units, of empty space in the cube?

Answer
A
4 thirds pi open paren 4 point 5 cubed close paren minus 4 point 5 cubed
B
9 cubed minus 4 thirds pi open paren 4 point 5 cubed close paren
C
4 thirds pi open paren 4 point 5 cubed close paren minus 9 cubed
D
9 cubed minus 4 thirds pi open paren 4 point 5 squared close paren

Explanation

The cube’s volume is 9³ cubic units. The sphere inside has radius 4.5 units, so its volume is (4/3)π(4.5³). Empty space is the cube’s volume minus the sphere’s volume, giving 9³ − (4/3)π(4.5³), the expression in choice A.

AI-written and checked against the verified answer.

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